Regarding the insurance policy premiums, presumably you were paying this via instalments. If you make a claim under the policy, you are obliged to continue paying until the policy expires, whether is is an annual policy or even a short term policy.
If it was your intention to cancel the policy shortly after its inception, in order to re-insure elsewhere, you would have been charged at a higher proportional rate, together with any administration charges, for a short term policy than for an annual policy.